Hey Muim, How you could do this and if it's possible depends on a few things, namely how you've set up your custom component and to what file type you're looking for. Retool does have two util functions that may be helpful here. Using utils.downloadPage you could download a PDF view of your chart on the page.
And using utils.downloadFile you could download the JSON itself as a 'json' file.
You could script either of these util functions in a JS query and pass them to your custom component. I hope that helps and if not, please let us know more about your custom component and how you're trying to download this chart!